HP 50G User manual

hp calculators
HP 50g Working with Fractions
Examples of Entering Fractions
Choosing the Right Modes
Examples of Fractions in RPN Mode
Example of Converting Fractions to Real Numbers
Example of Converting Real Numbers to Fractions
Example of Converting Real Numbers to Fractions
Involving PI
Accuracy, and an Example
Further Details

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HP 50g Working with Fractions
hp calculators - 2 - HP 50g Working with Fractions
Examples of Entering Fractions
To enter a fraction on the HP50g in Algebraic mode the user just types it. To enter 1/3, type this:
1/3`.
Calculating with fractions is just as easy. The HP50g knows the “rules of operator precedence”, which means that it carries out
divisions before additions, and gives the correct answer. Brackets can be used for greater clarity but are not needed just to show
what is a fraction. In Algebraic mode the HP50g automatically collects terms as well.
For example to add 2/3 to 5/7 it is enough to type
2/3+5/7`.
The answer 29/21 will be displayed. After these two calculations the HP50g should show:
Figure 1
Choosing the Right Modes
If the HP50g is not set to Exact mode then it is in Approximate mode, and the above will not happen. In Approximate mode exact
rational fractions are converted to their approximate decimal equivalents. Assuming that the display mode is set to STD, the
Standard mode, the second result will instead be shown as 1.38095238095
So, to work with fractions the HP50g should be in Exact mode. It recognizes numbers without decimal points as integers, and tries to
keep them as integers when working with rational numbers. If any number is typed with a decimal point, and Exact mode is set, the
HP48GII may ask whether the user wants to change to Approximate mode so that a non-integer answer can be calculated. The
HP48GII will not ask if flag –120 is set to silent mode on – it will automatically switch modes for you.
Figure 2
Pressing $OK$ to choose YES lets the HP50g switch to Approximate mode and give an answer. Pressing $CANCL$ or pressing the
down arrow key ˜and then pressing $OK$ to choose NO means the HP50g stays in Exact mode and can not calculate a non-
integer answer, so it will give an error message. To clear an error message, if one is displayed, press the $key to cancel the
error, then press the ƒkey to delete the message from the stack.
If the above question has been answered with a “YES”, or if Approximate mode has been set some other way, it is necessary to
change to Exact mode so that the examples in this training aid will display the correct answers. Press the Hkey and then press
the Ckey below the %CAS$ menu label. (CAS stands for Computer Algebra System, which is discussed in other training aids.)
Press the down key ˜twice to reach the APPROX label. If the label is checked, as in Figure 3, Approximate mode is set, so press
the Ckey below the $CHK% menu label to uncheck it. Then press the Fkey below the %OK% menu label to accept the change
to Exact mode.

hp calculators
HP 50g Working with Fractions
hp calculators - 3 - HP 50g Working with Fractions
Figure 3
The main Calculator Modes form will now be displayed. If the second line does not say STD then press the down arrow key once,
press Bbelow the !CHOOS menu label, use the up or down arrow to select STANDARD mode, and press the Fkey below the
%OK% menu label to accept the change to Standard mode. The Menu Form should now look as in Figure 4.
Figure 4
It is also worth checking the status of two system flags so that fractions are displayed as they should be. Press the Akey below
the !FLAGS menu label to change the flags. Press 5twice to reach flag 52, the second system flag whose number begins with a 5.
If flag 52 has a check mark by it, press the Ckey below the $CHK% menu label to uncheck it, so the menu looks as in Figure 5.
Figure 5
This changes from the “one line” display, which shows fractions as in Figure 1 to “many lines” display mode. Now use the down key
to reach flag 79, or press the 7key eight times. If flag 79 is checked, press the Ckey to uncheck it, so that its description
says “textbook on”. These two settings make the HP50g show fractions on two lines Press the Fkey below the %OK% menu label
to accept the flag settings. Press Fone more time to accept all the changes and quit the Calculator Modes form.
Now the calculator is in Exact mode and Standard mode. If the examples above did not give the expected answers, it is worth trying
them again. The HP50g is also in “many lines” and “textbook” modes now, so the fractions are shown on two lines.
Figure 6
Examples of Fractions in RPN Mode
To try the same examples in RPN mode, the user must first switch from Algebraic mode to RPN mode. Press the Hkey and then
press Bbelow the !CHOOS menu label, use the up or down arrow key to select RPN mode, then press the Fkey below the

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HP 50g Working with Fractions
hp calculators - 4 - HP 50g Working with Fractions
%OK% menu label to accept the change to RPN mode, and press the Fkey again to leave the Calculator Modes Form. Changing
back to Algebraic mode is done the same way, except that ALGEBRAIC should be selected instead of RPN in the Choose list.
Now type 2`3/ to see how the HP50g handles a fraction in RPN mode. It displays the fraction as in Algebraic mode.
Then type 5`7/+ to complete the same calculation as in Algebraic mode. The HP50g will show:
Figure 7
RPN works in step-by-step mode, so it does not automatically simplify the result, as Algebraic mode did. To simplify the result, use
the EXPAND command in the Algebra menu. Press …×to display the Algebra Menu, then select the EXPAND command from
the menu labels or press 2if you have CHOOSE boxes on. Then press the Fkey below the %OK% menu label. This simplifies
the expression, giving the same result as in Algebraic mode.
Here is another calculation to be tried in RPN mode. Type 3`4/ to see 3/4. Then type 2`6/ and the
result will be 1/3, which shows that simplification is carried out on single fractions. Multiplying the two by pressing *again gives a
combination of two fractions with no simplification.
Figure 8
An alternative to simplifying with the EXPAND command is to use the equation editor. Press Ito get the Tools menu keys at the
bottom of the display, as in Figure 8. Press the Akey below $EDIT# to see the expression in the equation editor.
Figure 9
Press Dbelow the #EVAL# menu label to evaluate the expression. Then press `to enter the evaluated value on the stack. As
expected, you will see ¼on the stack.
Tip! A way to type fractions directly when RPN mode is set is to press the ³key and then type the expression as in Algebraic
mode. To type the original example again, but as fractions in RPN, press ³2/3+5/7`. This takes
the same number of keys as doing it in pure RPN mode, pressing 2`3/5`7/+, but many users
feel it is more natural to type fractions as "numerator /denominator."
Example of Converting Fractions to Real Numbers
Whether the calculator is in Algebraic mode or In RPN mode, pressing …ï converts a fraction into the real number that is the
closest approximation possible on the HP50g. (A "real number" is a number with a decimal mark or an exponent, for example 1. or

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HP 50g Working with Fractions
hp calculators - 5 - HP 50g Working with Fractions
23.57 or 59.2E19. Only numbers typed without a decimal point are treated as integers by the HP50g, and fractions must be made up
of two integer numbers.) In RPN mode, the conversion is carried out immediately. In Algebraic mode, the result is presented in terms
of the ANS function. If the calculator is in RPN mode, it should be changed to Algebraic mode (as was described above) for this
example, then pressing …ï gives the answer with ANS(1) and pressing `gives the result.
Figure 10
Example of Converting Real Numbers to Fractions
The ->Q command converts a real number to a quotient, in other words into a fraction. The command can be found in the catalog of
commands, or it can be typed by using the ALPHA mode. If it is to be used often, it is best assigned to a key in the menu, or on the
User Keyboard. Ways to do this are described in other training aids.
To show the result of the previous calculation as a fraction, execute the ->Q command by using ALPHA mode. Press the keys below
and the result will be seen as in Figure 11.
~~…éq„Ü~„î`
Figure 11
Example of Converting Real Numbers to Fractions Involving PI
The command ->QΠwill convert a real number into a fraction multiplied by PI and another fraction not containing PI, and will then
give as its answer the fraction that is simpler. If the most recent result above is multiplied by PI, and converted to a real number then
->QΠwill convert the real number back to a fraction multiplying PI. First type
*„ì`…ï`
This converts 29Π/21 into a real number. Now type
~~…éq„ì„Ü~„î`
As Figure 12 shows, this really does convert the real number into a fraction multiplying PI.
Figure 12

hp calculators
HP 50g Working with Fractions
hp calculators - 6 - HP 50g Working with Fractions
If ->QΠwill convert a real number to whichever is better, a fraction with PI, or without, there may seem to be no reason to use ->Q.
In fact, there are two good reasons to use ->Q. The first is to use it where PI is not expected in the answer, and if it does appear, this
is purely by chance, and is not wanted. The second is in calculations that specifically try to convert PI itself into a fraction, as will be
shown in the next example. Thus ->QΠshould be used if there is an expectation that PI might be a part of the answer. If PI is not
wanted in the answer, ->Q should be used.
In RPN mode ->Q and ->QΠconvert a value from Level 1 of the stack to a fraction, possibly multiplied by PI if ->QΠis used.
Accuracy, and an Example
Converting a fraction to a real number with …ï always gives the most accurate representation of the fraction that is possible
on the HP50g. ->Q and ->QΠwill calculate the simplest fraction that they can find which gives a value as accurate as that shown in
the present display mode. If the number of digits shown in the display is increased then ->Q and ->QΠwill try to achieve the greater
precision and will often give a result that uses a longer numerator and denominator. This can be seen if PI is converted to a fraction
in different display modes.
First, it is necessary to set FIX 2 mode, where only 2 digits are shown after the decimal point. Press the Hkey and then press the
down key ˜to reach the number format. Press Bbelow the !CHOOS menu label, then use the up or down key to select FIXED
mode, and press the Fkey below the %OK% menu label to accept the change. Press the right arrow ™to reach the selection
for the number of digits, and press Bbelow !CHOOS again, then use the up and down keys to pick 2, and press Fbelow %OK%
again. Press Fonce more to confirm the whole selection and to leave the Calculator Modes Form.
Now to convert PI to a fraction in FIX 2 mode, in Algebraic mode, press „ì…ï to see 3.14. Then press ~~
…éq„Ü~„î`.
This will show 22/7, the well-known approximation to PI. To try the same with more accuracy, repeat the above process for setting
FIX 2 mode, but choose FIX 5 mode instead. To convert PI to a fraction in FIX 5 mode, press the same keys as before,
„ì…ï to see 3.14159. Press ~~…éq„Ü~„î`.
Now this will show 355/113, a better approximation to PI.
Figure 13
In both cases, the most accurate value of PI possible was on the stack, only the display was rounded to fewer decimal places, but in
each case ->Q returned the simplest value that could be found to represent PI to the accuracy displayed.
Once all the examples have been completed it may be worth returning the calculator to its normal modes. It can also be helpful to
clear the stack by pressing …·.
Further Details
->Q and ->QΠwill work with complex numbers and with expressions containing several real numbers. They will convert each real
number into a fraction separately. Note: ->QΠwill also convert real numbers in vectors and matrices to fractions.
The only way to guarantee that PI will appear when a real number is factored into a rational is to divide by PI first, then use ->Q, not
->QΠ. This is because of the way ->QΠworks. Most of the time this is not an issue, but there are situations where this must be
done if PI must be in the result.